Internet Analytics - Lab 2
Group: P
Names:
This is a template for part 3 of the lab. Clearly write your answers, comments and interpretations in Markodown cells. Don't forget that you can add $\LaTeX$ equations in these cells. Feel free to add or remove any cell.
Please properly comment your code. Code readability will be considered for grading. To avoid long cells of codes in the notebook, you can also embed long python functions and classes in a separate module. Don’t forget to hand in your module if that is the case. In multiple exercises, you are required to come up with your own method to solve various problems. Be creative and clearly motivate and explain your methods. Creativity and clarity will be considered for grading.
import networkx as nx
from networkx.readwrite import json_graph
import json
import epidemics_helper
import numpy as np
import matplotlib.pyplot as plt
import random
def read_json_file(filename):
with open(filename) as f:
js_graph = json.load(f)
return json_graph.node_link_graph(js_graph)
# ... WRITE YOUR CODE HERE...
G = read_json_file('../data/nyc_augmented_network.json')
sir = epidemics_helper.SimulationSIR(G, beta=10.0, gamma=0.1)
node_source = 23654
sir.launch_epidemic(source=node_source, max_time=100.0)
Epidemic stopped after 100.94 days | 100.94 days elapsed | 0.1% susceptible, 0.0% infected, 99.9% recovered
sir.rec_time
array([24.76681827, 11.63935766, 9.71325497, ..., 24.7443039 ,
9.88141307, 8.13479434])
def get_stats(G,sir):
infections = np.zeros(101)
recoveries = np.zeros(101)
for t in range(0,101):
for n in range(0,len(G.nodes)):
rec = int(sir.rec_time[n] < t)
recoveries[t] += rec
infections[t] += -rec
infections[t] += int(sir.inf_time[n] < t)
susceptibles = len(G.nodes) - infections - recoveries
return infections, recoveries, susceptibles
infections, recoveries, susceptibles = get_stats(G,sir)
x = range(0,101)
plt.figure('figure1',figsize=(7,5))
plt.plot(x, susceptibles / len(G.nodes) * 100, label = "Susceptibles")
plt.plot(x, recoveries / len(G.nodes) * 100, label = "Recoveries")
plt.plot(x, infections / len(G.nodes) * 100, label = "Infections")
plt.legend()
plt.xlabel('time')
plt.ylabel('cases (%)')
plt.grid()
plt.title('Epidemic evolution')
plt.show()
inf_60 = round(0.6*len(G.nodes))
inf_60
15889
def calc_60(infections,recoveries):
t_inf, t_rec = -1, -1
for t in range(0,101):
if infections[t] >= inf_60 and t_inf == -1:
t_inf = t
if recoveries[t] >= inf_60 and t_rec == -1:
t_rec = t
return t_inf, t_rec
t_inf, t_rec = calc_60(infections,recoveries)
print(f'The 60% of people will be infected on day = {t_inf}')
print(f'The 60% of people will be recovered on day = {t_rec}')
The 60% of people will be infected on day = 7 The 60% of people will be recovered on day = 15
dict_coord = {i:G.nodes[i]['coordinates'] for i in range(len(G.nodes))}
def select_color(node,t):
if sir.rec_time[node] < t:
return 'green'
if sir.inf_time[node] < t:
return 'red'
else:
return 'yellow'
plt.figure('figure1',figsize=(10,10))
color_map = []
for i in range(0,len(G.nodes)):
color_map.append(select_color(i,1))
nx.draw_networkx(G,pos=dict_coord, node_color=color_map, with_labels=False, node_size=10, alpha=0.5)
plt.title('Epidemics Graph at Day 1')
plt.axis('off')
(-74048875.915, -73831169.085, 40623760.05, 40926247.95)
At day 1, there are almost all susceptibles (in yellow color) and we can observe how the epidemic is expanding between the neighbours of the source node (red colour).
plt.figure('figure1',figsize=(10,10))
color_map = []
for i in range(0,len(G.nodes)):
color_map.append(select_color(i,3))
nx.draw_networkx(G,pos=dict_coord, node_color=color_map, with_labels=False, node_size=10, alpha=0.5)
plt.title('Epidemics Graph at Day 3')
plt.axis('off')
(-74048875.915, -73831169.085, 40623760.05, 40926247.95)
At day 3, the epidemic has started to infect the bridges and therefore other clusters. Some nodes have started to recover (in green).
plt.figure('figure1',figsize=(10,10))
color_map = []
for i in range(0,len(G.nodes)):
color_map.append(select_color(i,30))
nx.draw_networkx(G,pos=dict_coord, node_color=color_map, with_labels=False, node_size=10, alpha=0.5)
plt.title('Epidemics Graph at Day 30')
plt.axis('off')
(-74048875.915, -73831169.085, 40623760.05, 40926247.95)
At day 30, the epidemic has infected almost every node and the majority of them have already recovered from it.
# remove edges
def remove_rand_edges(graph,n):
for i in range(n):
edges = list(graph.edges)
chosen_edge = random.choice(edges)
graph.remove_edge(chosen_edge[0],chosen_edge[1])
return graph
G = read_json_file('../data/nyc_augmented_network.json')
sir = epidemics_helper.SimulationSIR(remove_rand_edges(G,1000), beta=10.0, gamma=0.1)
def calc_cv(m):
mean_rec = np.mean(m)
std_rec = np.std(m)
print(std_rec/mean_rec)
return std_rec/mean_rec >= 1.0
def mean_sim(G):
inf = []
rec = []
sus = []
means = []
i = 1
while i<7 or calc_cv(means):
i += 1
np.random.seed(i)
node_source = np.random.randint(0,len(G.nodes))
sir.launch_epidemic(source=node_source, max_time=100.0)
infections, recoveries, susceptibles = get_stats(G,sir)
inf.append(infections)
rec.append(recoveries)
sus.append(susceptibles)
means.append(recoveries[len(recoveries)-1])
inf_mean = np.array(inf).mean(axis=0)
rec_mean = np.array(rec).mean(axis=0)
sus_mean = np.array(sus).mean(axis=0)
return inf_mean,rec_mean,sus_mean
Here we compute the mean of the infections, recoveries and susceptibles in each iteration for each day of the epidemic.
Then, we have decided to fix the number of iterations based on the Coefficient of Variation (CV) of the recoveries at one day (we chose the last day).
When CV >= 1, indicates a relatively high variation of the recoveries, while a CV < 1 indicates a low variation. So when we reach CV < 1 we can say that the estimation is accurate.
We have decided to fix a minimum of 7 iterations.
inf_mean,rec_mean,sus_mean = mean_sim(G)
print()
print(f'On average the amount of people healthy people on day 30 is: {sus_mean[30]}')
print(f'On average the amount of people infected people on day 30 is: {inf_mean[30]}')
print(f'On average the amount of people recovered people on day 30 is: {rec_mean[30]}')
Epidemic stopped after 104.64 days | 104.64 days elapsed | 0.6% susceptible, 0.0% infected, 99.4% recovered Epidemic stopped after 101.67 days | 101.67 days elapsed | 0.6% susceptible, 0.0% infected, 99.4% recovered Epidemic stopped after 103.28 days | 103.28 days elapsed | 0.6% susceptible, 0.0% infected, 99.4% recovered Epidemic stopped after 107.08 days | 107.08 days elapsed | 0.7% susceptible, 0.0% infected, 99.3% recovered Epidemic stopped after 136.44 days | 136.44 days elapsed | 0.6% susceptible, 0.0% infected, 99.4% recovered Epidemic stopped after 102.92 days | 102.92 days elapsed | 0.6% susceptible, 0.0% infected, 99.4% recovered 0.00038655007618337026 On average the amount of people healthy people on day 30 is: 163.66666666666666 On average the amount of people infected people on day 30 is: 2754.0 On average the amount of people recovered people on day 30 is: 23563.333333333332
x = range(0,101)
plt.figure('figure1',figsize=(7,5))
plt.plot(x, sus_mean / len(G.nodes) * 100, label = "Susceptibles")
plt.plot(x, rec_mean / len(G.nodes) * 100, label = "Recoveries")
plt.plot(x, inf_mean / len(G.nodes) * 100, label = "Infections")
plt.legend()
plt.xlabel('time')
plt.ylabel('cases (%)')
plt.grid()
plt.show()
t_inf, t_rec = calc_60(inf_mean,rec_mean)
print(f'The 60% of people will be infected at time = {t_inf}')
print(f'The 60% of people will be recovered at time = {t_rec}')
The 60% of people will be infected at time = -1 The 60% of people will be recovered at time = 17
This strategy has decreased the number of people that gets infected (~3000 people less) by the COVID-19 because the number of edges between the nodes (people) have decreased.
# n = 10000
G = read_json_file('../data/nyc_augmented_network.json')
sir = epidemics_helper.SimulationSIR(remove_rand_edges(G,10000), beta=10.0, gamma=0.1)
inf_mean,rec_mean,sus_mean = mean_sim(G)
x = range(0,101)
plt.figure('figure1',figsize=(7,5))
plt.plot(x, sus_mean / len(G.nodes) * 100, label = "Susceptibles")
plt.plot(x, rec_mean / len(G.nodes) * 100, label = "Recoveries")
plt.plot(x, inf_mean / len(G.nodes) * 100, label = "Infections")
plt.legend()
plt.xlabel('time')
plt.ylabel('cases')
plt.grid()
plt.show()
Epidemic stopped after 108.59 days | 108.59 days elapsed | 24.9% susceptible, 0.0% infected, 75.1% recovered Epidemic stopped after 101.05 days | 101.05 days elapsed | 24.9% susceptible, 0.0% infected, 75.0% recovered Epidemic stopped after 100.69 days | 100.69 days elapsed | 57.4% susceptible, 0.0% infected, 42.6% recovered Epidemic stopped after 102.68 days | 102.68 days elapsed | 24.7% susceptible, 0.0% infected, 75.3% recovered Epidemic stopped after 105.17 days | 105.17 days elapsed | 83.9% susceptible, 0.0% infected, 16.1% recovered Epidemic stopped after 0.16 days | 0.16 days elapsed | 100.0% susceptible, 0.0% infected, 0.0% recovered 0.6427662477726126
On average there is a considerable decreasing on the number of infected people, but it depends a lot on which is the source node (the first infected person), if the nodes is part of a big cluster of nodes or if it is in a small one, in the first case there will be more infections than in the second case, or also if it has been affected for many removed edges.
def remove_bridge_edges(graph,n):
bridges = nx.local_bridges(graph)
bridge_sorted = sorted(bridges, key=lambda tup: tup[2])[-n:]
print(len(bridge_sorted))
for b in bridge_sorted:
graph.remove_edge(b[0],b[1])
return graph
G = read_json_file('../data/nyc_augmented_network.json')
sir = epidemics_helper.SimulationSIR(remove_bridge_edges(G,2500), beta=10.0, gamma=0.1)
2500
inf_mean,rec_mean,sus_mean = mean_sim(G)
Epidemic stopped after 113.56 days | 113.56 days elapsed | 83.6% susceptible, 0.0% infected, 16.4% recovered Epidemic stopped after 79.65 days | 79.65 days elapsed | 83.8% susceptible, 0.0% infected, 16.2% recovered Epidemic stopped after 93.79 days | 93.79 days elapsed | 58.0% susceptible, 0.0% infected, 42.0% recovered Epidemic stopped after 78.55 days | 78.55 days elapsed | 83.8% susceptible, 0.0% infected, 16.2% recovered Epidemic stopped after 98.26 days | 98.26 days elapsed | 86.2% susceptible, 0.0% infected, 13.8% recovered Epidemic stopped after 103.69 days | 103.69 days elapsed | 58.0% susceptible, 0.0% infected, 42.0% recovered 0.5096256227820168
x = range(0,101)
plt.figure('figure1',figsize=(7,5))
plt.plot(x, sus_mean / len(G.nodes) * 100, label = "Susceptibles")
plt.plot(x, rec_mean / len(G.nodes) * 100, label = "Recoveries")
plt.plot(x, inf_mean / len(G.nodes) * 100, label = "Infections")
plt.legend()
plt.xlabel('time')
plt.ylabel('cases')
plt.grid()
plt.show()
print(f'On average the % of people healthy people on day 30 is: {sus_mean[30] / len(G.nodes) * 100}')
print(f'On average the % of people infected people on day 30 is: {inf_mean[30] / len(G.nodes) * 100}')
print(f'On average the % of people recovered people on day 30 is: {rec_mean[30] / len(G.nodes) * 100}')
On average the % of people healthy people on day 30 is: 75.56109411779515 On average the % of people infected people on day 30 is: 1.8566771144090732 On average the % of people recovered people on day 30 is: 22.58222876779578
As we can see in this graph, we have managed to reach more than 70% of healthy nodes on average.
Here we are going to plot the evolution of the epidemic in our last simulation (58% of the people stayed healthy).
As we can see, it depends a lot in which giant component is the source node. In this case it is in a giant component with a lot of nodes that it much more connected than the giant components where the source nodes of the other simulations are.
We can also see how the removing of the local bridges has affected the connections between the giant components, isolating from of each other.
plt.figure('figure1',figsize=(10,10))
color_map = []
for i in range(0,len(G.nodes)):
color_map.append(select_color(i,1))
nx.draw_networkx(G,pos=dict_coord, node_color=color_map, with_labels=False, node_size=10, alpha=0.5)
plt.axis('off')
(-74048875.915, -73831169.085, 40623773.31, 40926246.69)
plt.figure('figure1',figsize=(10,10))
color_map = []
for i in range(0,len(G.nodes)):
color_map.append(select_color(i,3))
nx.draw_networkx(G,pos=dict_coord, node_color=color_map, with_labels=False, node_size=10, alpha=0.5)
plt.axis('off')
(-74048875.915, -73831169.085, 40623773.31, 40926246.69)
plt.figure('figure1',figsize=(10,10))
color_map = []
for i in range(0,len(G.nodes)):
color_map.append(select_color(i,30))
nx.draw_networkx(G,pos=dict_coord, node_color=color_map, with_labels=False, node_size=10, alpha=0.5)
plt.axis('off')
(-74048875.915, -73831169.085, 40623773.31, 40926246.69)
